发表机构
CSIRO Technology Research Way, Clayton VIC 3168, Australia; School of Computing and Information Systems The University of Melbourne; School of Physics, Mathematics and Computing The University of Western Australia（澳大利亚CSIRO技术研究路; 墨尔本大学计算机与信息系统学院; 西澳大学物理、数学与计算学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对矩阵值输入，引入量子谱模型，直接从输入矩阵构建数据编码酉矩阵生成器，基于不同哈密顿量研究三种变体。在多个任务上评估其与其他量子模型，结果表明QSM变体表现出色，为量子机器学习模型设计提供新视角。
AI 中文摘要
现代机器学习和人工智能的核心设计原则是使模型的归纳偏差与输入数据结构对齐。对于矩阵值输入，相关矩阵级关系可通过谱值和谱子空间表征，但多数量子机器学习模型常用的坐标旋转门数据编码酉矩阵未明确构建此类矩阵级表示。我们引入量子谱模型（QSM），直接从每个输入矩阵构建数据编码酉矩阵的生成器。研究了基于对称、全局块和非重叠补丁局部块哈密顿量的三种QSM变体。其输出允许截断傅里叶表示，输入相关谱隙提供候选相位载波，谱子空间帮助确定系数。在两个Pendigits矩阵表示和两个由谱统计定义的受控合成任务上评估了QSM和比较量子模型。在最大评估电路深度下，QSM变体在所有四个基准测试的平均测试准确率上领先于测试的量子模型。补丁局部QSM在Pendigits上领先，全局块哈密顿量QSM在受控谱任务上领先。消融实验显示任务相关的反转：保留子空间的控制在Pendigits上表现更好，而仅谱值控制在合成任务的测试消融中领先。这些结果通过展示输入条件谱表示如何提供可分析的归纳偏差，为量子机器学习模型设计提供了新视角，同时为机器学习和人工智能中的结构感知模型设计提供了更广阔的视角。
英文摘要
A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral subspaces; however, common coordinate-wise rotation-gate data-encoding unitaries used in most quantum machine learning models do not explicitly construct such a matrix-level representation. We introduce Quantum Spectral Models (QSMs), in which we construct the generator of the data-encoding unitary directly from each input matrix. We study three QSM variants based on symmetric, global block, and non-overlapping patch-local block Hamiltonians. Their outputs admit truncated Fourier representations in which input-dependent spectral gaps supply candidate phase carriers, while spectral subspaces help determine their coefficients. We evaluate the QSMs and comparison quantum models on two matrix representations of Pendigits and two controlled synthetic tasks defined by spectral statistics. At the largest evaluated circuit depth, QSM variants lead the tested quantum models in mean test accuracy across all four benchmarks. The patch-local QSM leads on Pendigits, whereas the global block-Hamiltonian QSM leads on the controlled spectral tasks. Ablations show a task-dependent reversal: subspace-preserving controls perform better on Pendigits, whereas spectral-value-only controls lead among the tested ablations on the synthetic tasks. Together, these results shed new light on quantum machine-learning model design by showing how input-conditioned spectral representations can provide an analysable inductive bias, while offering a broader perspective on structure-aware model design in machine learning and artificial intelligence.
Comments53 pages, many figures
